[Zurück]

F. Ziegler:
"The multiple field concept of structural analyses: an outlook on deformation control.";
Vortrag: 5th World Congress on Computational Mechanics, Vienna; 07.07.2002 - 12.07.2002; in: "Proceedings of WCCM V - Fifth World Congress on Computational Mechanics", H.A. Mang, F. G. Rammerstorfer, J. Eberhardsteiner (Hrg.); (2002), ISBN: 3-9501554-0-6.

Static and dynamic processes in linearized thermo-elasticity have been explored in detail. Interpreting the thermal strain as a source in the isothermal background structure renders a simple multiple field analysis in a classical setting. Analogously, all kinds of non-compatible strains (strain rates), e. g., of a viscoplastic deformation with or without ductile damage taken into account, can be considered in the form of distributed sources in the linear elastic background. Turning to dynamics, a direct multiple field analysis of uniaxial elastic-plastic waves is presented with the extension to spherical waves indicated. Even in a three-dimensional setting, the waves sent out by an instantaneous localized plastic source are identified for a fixed receiver station by a time convolution. The kernel is the Green’s function commonly of the second kind and contains all the information of the background wave guide. For layered plates an expansion into plane waves renders a working tool of in-depth analysis. Applications seem to be promising in the field of monitoring of elasti-plastic structures which may be subjected to overloads. Most importantly, however, in vibrational problems, the superposition principle is (incrementally) applicable despite of the actual material nonlinearity, and the solution is split into the quasistatic one (no inertia is taken into account) and the dynamic one. In such a case, the dynamic boundary conditions can be made homogeneous and the dynamic solution might be suitably well documented by taking a low order modal expansion into account. The analyses are either based on the differential equations of motion with the linear operator of the background structure on the left hand side and the forcing terms including the distributed sources on the right hand side or on reciprocity theorems e.g. in the form of the generalized Maysel's formula well known from linear thermoelasticity. An important application refers to interface slip of vibrating layered (slender) structures, like composite beams, plates or shells. Such a multiple field formulation is extremely well suited to enter the field of quasi-static or dynamic deformation control by distributed actuators. Controlled heating of members in frames or trusses of space structures for slow processes (without additional thermal stresses) or application of the piezoelectric effect in composite 'thin-walled" structures like beams, plates and shells also for rapid loading, all are considered by the integral equation approach. In special cases the cumbersome nonlinear optimization procedure is saved at all. However, the ill-posed problem affects also this direct approach through non-uniqueness.

http://wccm.tuwien.ac.at